Advertisements
Advertisements
प्रश्न
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
`sin^-1 [cos(sin^-1 1/2)] = sin^-1 [cos(sin^-1 sin pi/6)]`
`sin^-1 [cos pi/6] = sin^-1 (sqrt(3)/2)`
= `sin^-1 (sin pi/3)`
= `pi/3`
APPEARS IN
संबंधित प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
The principal solution of the equation cot x=`-sqrt 3 ` is
Find the principal value of the following:
`sin^-1(-sqrt3/2)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
Find the value of `sec(tan^-1 y/2)`
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
The value of `sin^-1 (cos((43pi)/5))` is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of cot (sin–1x) is ______.
The domain of sin–1 2x is ______.
The value of sin (2 sin–1 (.6)) is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Which of the following is the principal value branch of cos–1x?
Which of the following is the principal value branch of cosec–1x?
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
